Line integral Definition and 393 Threads

Homework Statement Calculate the line integral of A between to points x=1 and x=3 along the semicircular path with a center at x=2 Homework Equations A=kx in the x hat direction. \int A \bullet dl dl = ds s hat +s d\phi \phi hat +dz z hat The Attempt at a Solution My...

Homework Statement \inty dx +x dy + z dz c= helix x = 3 cos t y = 3 sin t z = 4t 0\leqt\leq2\Pi Homework Equations \int F(x,y,z) ds ds=\sqrt{[Fx(x,y,z)]+[Fy(x,y,z)]+[Fz(x,y,z)]}dt (still learning latex the partial derivatives are suposed to be...

EDIT: SORRY, I didn't read the directions. It says, "Answer the following short questions: If true, justify, if false give a counterex- ample." I'm certain that this question is one of the "false" ones, which is why I was so confused. LOL Homework Statement Let f(x, y, z) = y - x. Then the...

Evaluate the line integral \int F \circ dr for (a) F(x,y) = (x - y) * i + xy * j and C is the top half of a circle of radius 2. Here's green's theorem. Double integral ( dQ/ dx - dP/dy) dA dQ/dx = y dP /dy = -1 It becomes ∫∫ (y +1) dA y = r sin Θ so...

Well i know that the line integral is given a scalar function f. equation1 But the line integral is also given a vector field F. equation2 So, given scalar function f and taking the gradient vector of it in order to turn it into a vector field F. Why is equation1 not equal to equation2?

Homework Statement Integrate along the line segment from (0,0) to (\pi,-1) The integral \int_{(0,1)}^{(\pi,-1)} [y sin(x) dx - (cos(x))]dy Homework Equations The Attempt at a Solution I have used the parameterization of x=\pi t and y= 1-2t To get the integral...

Homework Statement A particle is attracted towards the origin by a force proportional to the cube of its distance from the origin. How much work is done in moving the particle from the origin to the point (2,4) along the path y = x^2 assuming a coefficient of friction \mu between the particle...

Homework Statement Let F=(3x+2y)i+(2x-y)j Evaluate \int_{C}F . dr where C is the line segment from (0,0) to (1,1) Homework Equations \int_{a}^{b}[f(x(t),y(t))x'(t) + g(x(t),y(t))y'(t)]dt The Attempt at a Solution How do I choose the correct values of x and y as a function...

Hello Everyone I have a few questions regarding line integrals. First what are they? What is the difference between them and the normal integrals? For eg, The normal integrals can be easily understood by visualizing the area bounded by them, in the same way is there any way as to visualize the...

Not exactly a homework problem, a problem from a sample test. I'm boning up for my qualifying exam. Homework Statement Consider the vector field: F = (ax + by)i + (cx + dy)j where a, b, c, d are constants. Let C be the circle of radius r centered at the origin and going around...

Homework Statement Let f(x,y,z) be a function of three variables. Suppose that C is an oriented curve lying on the level surface f(x,y,z) = 5. Find the integral grad f dot dr. Homework Equations The Attempt at a Solution integral grad f dot dr = integral f(q) - f(p) not...

Hello all, I am trying to solve a line integral: Find the value of \int -2y dx + x^2 dy over the circle x^2 + y^2 = 9 as you can see, this is a line integral, and I am trying to figure a quick way how it should be solved. I thought of converting coordinates to (sint,cost) which will...

Homework Statement Find the work doneby the force field F on a particle that moves along the curve C. F(x,y)=xy i + x^2j C: x=y^2 from (0,0) to (1,1) Homework Equations \intF dot dr=\int^{b}_{a}F(r(t))dotr'(t)dt The Attempt at a Solution Okay, so I parametrized x=t and y=t^2...

Let C be the triangle in the plane from (0,0) to (1,1) to (0,1) back to (0,0). evaluate the line integral of f along C if f(x,y)=(x+2y). attempt: C1: x=t y=t ds=root(1)dt, integrated t+2t from 0 to 1 to get 3/2 C2: x=-t ds=root(1)dt, integrated -t from -1 to 0 to get 1/2 C3: y=-t...

Let C be the line segment from (0,0,0) to the point (1,3,-2). evualuate the line integral of f along C if f(x,y) = (x + y^2 -2z) so far i was able to write the parametric form x = t y=3t and z=-2t the square root of all the derivatives is root(14). so i get root(14) times integral of...

Homework Statement A curve lamda starts in (0,0) and fallows a straight line from x = 0, y = 0 to x = 1, y = 0 and then another straight line to x = 2 and y = 1. Calculate the line integral I = S vdr where S is an integral s v = (x+3y)i + (3+y)j Homework Equations...

Homework Statement http://img7.imageshack.us/img7/1764/capkgc.th.jpg Homework Equations The Attempt at a Solution Okay I already got the result for the line integral along the circle, but I am confused how to get the line integral in the x-axis? To get the final result I just...

I'm a bit confused as to how to solve this line integral: Evaluate I = The integral of (x+y)dx from A (0,1) to B (0,-1) along the semi-circle x^2 + y^2 = 1 for for x is equal to or greater than 0. So far have have got: if x^2 + y^2 = 1 then y= + SQRT of (1 - x^2) which I believe...

Homework Statement I am trying to solve a line integral (bear with me, I am new to calculus!) and my basic skills of integration seem to fail me. I am sure the mistake is quite obvious, as I keep getting the wrong answer, 2, when it should be ~2.69 Homework Equations \int_C 4x^3dS C is the...

I have just begun exploring the topic of line integrals for my Calculus 3 class. Although I can perform the calculation properly, I don't understand the physical significance of what I've just calculated. For example, I know that when I calculate the integral of a function which is defined...

Homework Statement Consider the vector potential A = cr * [(sin theta)^2 * (cos fi) * (sin fi) + (cos theta)^2 ) er + (sin theta) cos (theta) * [(sin fi) (cos fi)  − 1] e theta + {(sin theta) (cosfi)^2 } efi er: in the er direction e theta: in the e theta direction...

I have to evaluate the line integral : \oint_{}^{} (2x + y)dx + xydy between (-1,2) and (2,5) on the curve: y = x + 3 So, what I did was: \int_{-1}^{2} (3x+3)dx + \int_{2}^{5} (x^{2} + 3x)dx However, this is wrong and I am not sure why! Can someone please guide me? Thanks alot!

Homework Statement Evaluate the line integral \[ \int_c yz\,ds.\] where C is a parabola with z=y^2 , x=1 for 0<=y<=2Homework Equations A hint was given by the teacher to substitute p=t^2 , dp=(2t)dt and use integration by parts. I also know from other line integrals with respect to arc length...

Homework Statement The force exerted by an electric charge at the origin on a charged particle at point (x,y,z) with position vector r = <x,y,z> is F(r) = Kr / |r|^3 where K is a constant. Find the work done as the particle moves along a straight line from (2,0,0) to (2,1,5). Homework...

Homework Statement For the field \bold{F} = (y+z) \bold{i} - (x+z) \bold{j} + (x+y) \bold{k} find the work done in moving a particle around the following closed curve: from the origin to (0,0,2π) on the curve x=1-cos t, y=sin t, z=t; and back to the origin along the z-axis. The answer is 2π...

Homework Statement The cyclotron is a device for accelerating charged particles. It requires changing electric fields and a magnetic field, but it can be modeled using (non-physical) static electric fields and potentials as we will do in this problem. Keep in mind that these fields cannot...

Homework Statement There is a constant electric field E = E0sin(kz+wt+pi/3) k(direction vector). What is the value of the line integral(P) B.dl, where P is a circular path, centered on the origin, lying in the xy-plane, having radius r? Homework Equations integral E.dl = -dI/dt The...

Recently I was working through a problem involving a force field, and came up with a question I could not answer, so I thought I would post it here. I solved the problem using a vector representation and a line integral, and although I am sure the answer is correct, I would like to solve it by a...

Greetings, I'm having trouble deciding what to do, and in what order for this question: Suppose F = F( x, y, z ) is a gradient field with F = \nablaf, S is a level surface of f, and C is a curve on S. What is the value of the line integral (over C) of F.dr ? I think I'm a little confused...

Homework Statement What is the line integral of F(x,y,z) = (xy, x, xyz) over the unit circle c(t) = (cost, sint) t E (0,2pi) ? Homework Equations integral= (f(c(t))*c'(t))dt) The Attempt at a Solution Ok, so I tried solving this like I would any other line integral using the given...

Homework Statement Calculate the anti-derivative of ydx where c in the ellipse 4x^2 + 25y^2 = 100 Homework Equations Definition of a line integral The Attempt at a Solution I tried parameterizing the equations but I sure if am making the right choice

Hi all, I'm new to the forums so if i do something stupid don't hesitate to tell me. Anyway I'm struggling with this problem: I could do part a ok, but part b has me stumped, I am in the second year of a physics degree and this is a from a maths problem sheet, i haven't done line...

a curve is given as 3 parameters of t: x=a(3t - t^3), y=3a(t^2), z=a(3t + t^3) i have to find the arc length measured from origin and curvature as functions of t. would i be correct in using the integral at the bottom of page 2 here: http://homepages.ius.edu/wclang/m311/fall2005/notes17.2.pdf

Homework Statement Evaluate the line integral, where C is the given curve: \int_C\,y\,ds \, \,\,\,\,C:\,x=t^2\,\,\,\,y=t for t between 0 and 2 (out of curiousity, how do you make the "greater than or equal 2" in LateX) Okay, in the book the line integral is defined as \int_C F\cdot...

Homework Statement given the vector A = 4r + 3theta -2phi , find its line integral around the closed path. (the figure contained in the book is a straight line along the x-axis extending to radius a, with a curved portion of a circle with radius a centered at the origin curving back to the...

Hey guys! I have been on the forum for about a week or so and have compiled a lot of information and techniques to help me understand calculus, so i really appreciate everyone's help! I am a soon-to-be freshman in college and am taking a summer class, calculus II (took calc I in HS). This is...

How would you DEFINE the line integral: int_aroundc[P(x,y)dx + Q(x,y)dy]

Homework Statement A 160-lb man carries a 25-lb can of paint up a helical staircase that encircles a silo witha radius of 20 ft. If the silo is 90 ft high and the man makes exactly three complete revolutions, how much work is done by the man against gravity in climbing to the top...

Homework Statement Evaluate the line integral, where C is the given curve. integral of xy^4. C is the right half of the circle x^2 + y^2 =16 Homework Equations integral of line integral= integral of r(t) |r'(t)| dtThe Attempt at a Solution I set up a parametric equation to be r(t)=(4cost...

"Stokes theorem" equivalent for cross product line integral Homework Statement I am aware that the vector path integral of a closed curve under certain conditions is equivalent to the flux of of the curl of the vector field through any surface bound by the closed path. In other words, Stokes...

Homework Statement A region R is bounded by the curves y = 12.x and y=5.x^2 If I = (5/12).x^2 .y i + (y/12.x) j find the contribution to the line integral Integral I.dl = Integral (I(x) dx + I(y) dy) taken in the anti clockwise direction with respect to the region R along the curve...

Homework Statement Integrate f(x,y) = (x^3)/y over the curve C: y = (x^2)/2, 0 <= x <= 2 Homework Equations The Attempt at a Solution So far I'm only familiar with line integrals over space curves such as questions like this: Find the line integral of f(x,y,z) = x + y + z over the...

Homework Statement Evaluate the line integral by two methods: (a) directly and (b) using Green's Theorem. \oint_C {xy^2 \,dx\, + \,x^3 \,dy} . C is the rectangle with vertices (0,0), (2,0), (2,3) and (0,3). The Attempt at a Solution I get the correct answer using Green's theorem. But I...

1. Evaluate the line integral∫F . dr with F = 3(-y,x,0) from (a,0,0) to (a,0,2πb) along a straight line. 2. Do the same along a circular helix between the two points, parameterised as r = (a cosλ, a sinλ, bλ) 3. Compute the curl of F. How does this relate to the two integral calculations...

1.Homework Statement (Parabolic Cylinder) find the area of the surface extending upward form x^2 + y^2 =1 to z = 1 - x^2 using line integral 2. Could some one please outline the method to solving this. I tryed using spherical corridinates but am unsure if this was correcect The...

Hiya, I've just done a line integral question, and the final part of the question is, "by applying a standard test, determine whether the value of the line integral depends on the path followed between the given initial and final points." The only standard test, I know, is dq/dx, and dp/dy to...

Homework Statement It can be shown that the line integral of F = xj around a closed curve in the xy - plane, oriented as in Green's Theorem, measures the area of the region enclosed by the curve. (You should verify this.) Use this result to calculate the area within the region of the...

Homework Statement What is the line integral of B between points i and f in the figure? Homework Equations Ampere's Law: ∫B∙dl = Ienclosed * μ0 note: the integral on the left is a line integral. The Attempt at a Solution I applied Ampere's Law. I know that the contribution...

Hello! I am working on atmospheric scattering and therefore I have to calculate the optical depth along a given path through the atmosphere. The integral I have to solve is this one: \int_{P_a}^{P_b} f ds \quad with \quad f:R\rightarrow R, h\rightarrow e^{(-h/H_0)} P_a und P_b are...

Homework Statement Compute the line integral of v = 6i + yz^2j + (3y + z)k along the path (0,0,0) -> (0,1,0) -> (0,0,2) -> (0,0,0). Check your answer using Stokes' Thm Homework Equations The Attempt at a Solution I've tried breaking into three pieces. The first with dx = dz =...